Empirical Description of Node-to-Node Distance Density in Non-Overlapping Wireless Networks

In wireless communications, knowledge of the node-tonode distance is essential in tasks such as system configuration, protocol design, and performance analysis. In this paper, we empirically describe the distance density between nodes in nonoverlapping networks under the assumptions of circular coverage area and uniform node distribution. In general, this problem has no closed-form solution. Here, we approximate it with polynomial expressions by applying curve fitting on a large set of simulation traces. The impact of network size on distance statistics is investigated. We also discuss an application in path loss modeling. The results of this paper are of practical value for the design and performance analysis of wireless networks. The derived closedform expressions achieve a significant reduction in the complexity and computational cost of the modeling and simulation of wireless communications systems; moreover, the simulation results provide some insight into the nature of radio signal propagation.